a) Ta có :
\(\left(8x-1\right)^{2n+1}=7^{2n+1}\)
\(\Leftrightarrow8x-1=7\)
\(\Leftrightarrow8x=8\)
\(\Leftrightarrow x=1\left(tm\right)\)
Vạy ..........
2) \(5^x.\left(5^3\right)^2=625\)
\(\Leftrightarrow5^x.5^6=625\)
\(\Leftrightarrow5^{x+6}=5^4\)
\(\Leftrightarrow x+6=4\)
\(\Leftrightarrow x=-2\left(tm\right)\)
Vậy ...............
3) \(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)
\(\Leftrightarrow\left(x-7\right)^{x+1}.\left[1-\left(x-7\right)^{10}\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\\left(x-7\right)^{10}=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\\left[{}\begin{matrix}x-7=1\\x-7=-1\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=7\\\left[{}\begin{matrix}x=8\\x=6\end{matrix}\right.\end{matrix}\right.\)
Vậy ..
1,(8x-1)2n+1=72n+1
=>8x-1=7
=>8x=8
=>x=1
Vậy x=1
\(\left(8x-1\right)^{2n+1}=7^{2n+1}\)
\(\Rightarrow8x-1=7\Rightarrow8x=8\Rightarrow x=1\)
\(5^x.\left(5^3\right)^2=625\)
\(\Rightarrow5^x.5^6=625\)
\(\Rightarrow5^{x+6}=625\)
\(\Rightarrow5^{x+6}=5^4\)
\(\Rightarrow x+6=4\Rightarrow x=-2\)
\(\left(x-7\right)^{x+1}=\left(x-7\right)^{x+11}\)
\(\Rightarrow\left(x-7\right)^{x+11}-\left(x-7\right)^{x+1}=0\)
\(\Rightarrow\left(x-7\right)^{x+1}\left[\left(x-7\right)^{10}-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-7\right)^{10}=0\Rightarrow x=7\\\left(x-7\right)^{10}-1=0\Rightarrow x-7=\pm1\Rightarrow x=8;6\end{matrix}\right.\)
Dễ làm nốt nha
2,
5x.(53)2=625
=>5x.56=625
=>5x+6=54
=>x+6=4
=>x=-2
Vậy x=-2
